Elastic Momentum Transfer Cross Sections Research Articles

Theoretical study of low-energy electron collision with normal-pentane using R-matrix method

Low-energy electron collisions with normal-pentane (n-C5H12) that initiate the plasma to assist combustion are critical in understanding the underlying physics and chemistries. In the present work, we studied this collisional process using the R-matrix method at the static-exchange plus polarization and close-coupling model levels. The scattering calculation was performed by running the UKRmol+ code using the Quantemol Electron Collision interface to obtain elastic differential, momentum transfer, integral, and electronic excitation cross sections up to 20 eV and ionization cross sections up to 1000 eV. Our computed cross-section data are in better agreement with the available experimental results both regarding the magnitude and shape. We also demonstrated the importance of using a diffuse basis set in describing the scattering due to the Rydberg nature of the lowest unoccupied molecular orbitals of n-C5H12.

Elastic and inelastic low-energy electron scattering from pyridine.

A comprehensive investigation of elastic and inelastic electron scattering from molecular pyridine is reported using the ab initio R-matrix method with the static exchange plus polarization and close-coupling approximations for incident energies up to 10eV. The two well-known low-lying 1 2B1 and 1 2A2 shape resonances as well as a 2 2B1 mixed-character resonance compare well with the theoretical and experimental results. We also detect five core-excited resonances (1 2A1, 1 2B2, 3 2B1, 2 2A2, and 4 2B1), which lie above the first electronic excitation threshold. The total elastic cross sections and momentum transfer cross sections agree reasonably with previous reference data. Comparisons of the differential elastic cross sections of pyridine with those measured for benzene, pyrazine, and pyrimidine show remarkable agreement at scattering angles above 40° but behave differently for forward scattering below 40° below 6eV, due to the dominant effect of the permanent dipole moment on the differential cross section in the low energy region with narrow scattering angles. Inelastic electronic excitation cross sections are presented, showing the influence of core-excited resonances below the ionization threshold for the first time.

Joint experimental and theoretical study on electron scattering from titanium tetrachloride (TiCl4) molecule.

Absolute grand-total cross section for electron scattering from titanium tetrachloride, TiCl4, molecule was measured at electron-impact energies ranging from 0.3 to 300eV, in the linear electron-transmission experiment. The elastic integral, differential, momentum transfer, and total ionization cross sections for TiCl4 molecule were also calculated for low and intermediate collisional energies at the level of various theories. The low-energy elastic integral, differential, and momentum transfer cross sections were calculated with the Schwinger multichannel method implemented with pseudopotentials, in the static-exchange and static-exchange plus polarization levels of approximation, for energies up to 30eV. The integral cross section calculated for low-energy electron scattering with the R-matrix method within the static-exchange and static-exchange plus polarization approximations for energies up to 15eV are also reported. By the inspection of the cross sections, the presence of resonances is discussed. In particular, the calculated integral cross sections and the measured total cross section display a minimum at around 1eV, which is consistent with the presence of a Ramsauer-Townsend minimum and a sharp increase at low energies, which is consistent with the presence of a virtual state. Additionally, interactions in elastic and ionization channels for intermediate collision energies were investigated with the additivity rule and the binary-encounter-Bethe methods.

Electron impact cross-sections of tetraethyl silicate

Understanding the interactions of electrons with molecules in plasma is of vital importance from both academic and technological points of view. Reliable electron collision data is required to model the electron and ion components of low-temperature and nonequilibrium plasmas. Various electron impact cross sections such as the differential, integral, momentum transfer, partial and total ionizations are reported for tetraethyl silicate (TEOS), a plasma-relevant molecule in the energy range between the ionization threshold and 5 keV. The elastic (differential, integral and momentum transfer) cross sections are obtained by invoking the molecular approach and local potential approximation within the single center expansion formalism. The dissociative ionization cross sections are reported within the binary encounter Bethe (BEB) model formalism. The elastic and ionization cross sections are summed incoherently to estimate total cross sections. A good agreement is observed between the present results and others that are available. This work validates the efficacy of the modified BEB model in computing the partial ionization cross sections.

Elastic and Inelastic Cross Sections for Low-Energy Electron Collisions with ClF Molecule Using the R-Matrix Method

The ClF molecule belongs to an interhalogen family and is important in laser physics and condensed phase molecular dynamics. The elastic and excitation scattering cross sections are obtained in a fixed nuclei approximation using the UKRmol+ codes based on R-matrix formalism. The scattering calculations were performed in the static-exchange (SE), static-exchange-plus-polarisation (SEP), and close-coupling (CC) models. Three CC models with different target states were employed, namely, the 1-state, 5-states, and 12-states. In the CC model, the target states were represented by configuration interaction (CI) wavefunctions. A good agreement of dipole and quadrupole moments of the ground state was obtained with the experimental values, which indicates a good representation of the target modelling. The study predicted the existence of a shape resonance in the SE, SEP, and 5-states CC models. This resonance vanished in the 12-states CC model. The excitation cross sections from ground to the lowest two excited states were also reported. The elastic differential and momentum transfer cross sections were obtained in the 12-states CC models. The contribution of long-range interactions to elastic scattering was included via Born closure approach. The quantities like collision frequencies and rate coefficients were also presented over a wide range of electron temperatures. The ionization cross sections were computed using the binary-encounter-Bethe (BEB) model. The results were reported in C2v point group representation.

Extracting electron scattering cross sections from swarm data using deep neural networks

Electron-neutral scattering cross sections are fundamental quantities in simulations of low temperature plasmas used for many technological applications today. From these microscopic cross sections, several macro-scale quantities (called ‘swarm’ parameters) can be calculated. However, measurements as well as theoretical calculations of cross sections are challenging. Since the 1960s, researchers have attempted to solve the inverse swarm problem of obtaining cross sections from swarm data; but the solutions are not necessarily unique. To address these issues, we examine the use of deep learning models which are trained using the previous determinations of elastic momentum transfer, ionization and excitation cross sections for different gases available on the LXCat website and their corresponding swarm parameters calculated using the BOLSIG+ solver for the numerical solution of the Boltzmann equation for electrons in weakly ionized gases. We implement artificial neural network (ANN), convolutional neural network (CNN) and densely connected convolutional network (DenseNet) for this investigation. To the best of our knowledge, there is no study exploring the use of CNN and DenseNet for the inverse swarm problem. We test the validity of predictions by all these trained networks for a broad range of gas species and we deduce that DenseNet effectively extracts both long and short term features from the swarm data and hence, it predicts cross sections with significantly higher accuracy compared to ANN. Further, we apply Monte Carlo dropout as Bayesian approximation to estimate the probability distribution of the cross sections to determine all plausible solutions of this inverse problem.

Electron collision cross section set for N2 and electron transport in N2, N2/He, and N2/Ar

Electron collision cross section set for N2 is proposed. The proposed set consists of vibrational elastic momentum transfer cross section and cross sections for 31 rotational excitation, 29 rotational deexcitation, 10 vibrational excitation, 17 electronic excitation, 2 neutral dissociation, and 5 ionization collision processes. Electron transport coefficients in N2, N2/He, and N2/Ar are calculated by Monte Carlo method with considering anisotropic inelastic electron scattering and partitioning of the residual energy after the ionization collision on the basis of experimental results. The reliability of the proposed electron collision cross section set is demonstrated by comparing the calculated and measured electron transport coefficients in a wide range of reduced electric fields, E/N (E: electric field strength, N: number density of gas molecules). Comparison of the values of the electron transport coefficients in N2 calculated from eight individual cross section sets partly provided on LXCat with the measured values is also carried out. Furthermore, the effect of anisotropic inelastic electron scattering on the electron transport coefficients is examined. The electron transport coefficients in N2 are found to be affected by considering anisotropic electron scattering with increasing E/N values, and the longitudinal third-order transport coefficient is found to be sensitive to considering anisotropic electron scattering even at middle E/N values.

Recommended Cross Sections for Electron–Indium Scattering

We report, over an extended energy range, recommended angle-integrated cross sections for elastic scattering, discrete inelastic scattering processes, and the total ionization cross section for electron scattering from atomic indium. In addition, from those angle-integrated cross sections, a grand total cross section is subsequently derived. To construct those recommended cross-section databases, results from original B-spline R-matrix, relativistic convergent close-coupling, and relativistic optical-potential computations are also presented here. Electron transport coefficients are subsequently calculated, using our recommended database, for reduced electric fields ranging from 0.01 Td to 10 000 Td using a multiterm solution of Boltzmann’s equation. To facilitate those simulations, a recommended elastic momentum transfer cross-section set is also constructed and presented here.

Elastic-electron-scattering from 1,2-ethylenediamine and dimethyldiazene

We present elastic integral, differential and momentum transfer cross sections for scattering of electrons by 1,2-ethylenediamine (NH2C2H4NH2) and by dimethyldiazene (CH3N2CH3). The cross sections were computed with the Schwinger multichannel method implemented with norm-conserving pseudopotentials. The calculations were carried out in the static-exchange and static-exchange plus polarization approximations for energies up to 20 eV. We found the presence of a Ramsauer–Townsend minimum at around 0.38 eV in the integral cross section of 1,2-ethylenediamide and a π* shape resonance at around 1.0 eV in the integral cross section of dimethyldiazene, both cross sections computed in the static-exchange plus polarization approximation. In the static-exchange approximation the resonance is located at 3.5 eV. For dimethyldiazene we also employed an empirical scaling relation to estimate the vertical attachment energy and the value of 1.1 eV agree well with the position of the resonance of 1.0 eV obtained through the scattering calculation. We compare our results with recent calculations [G. L. C. de Souza, J. Electron Spectrosc. Relat. Phenom. 234, 64 (2019)] and found in general a very good agreement in the shape of the cross sections, but there are some discrepancies regarding their magnitude.

Electron and Positron Scattering by the Formamide Molecule.

We report calculated elastic integral, differential, and momentum transfer cross sections for electron and positron collisions with the formamide (HCONH2) molecule, for impact energies up to 10 eV. We have used the Schwinger multichannel method in the static-exchange and static-exchange plus polarization approximation for collisions of electrons and the static plus polarization approximation for collisions of positrons. The Born-closure procedure was applied to account for the long-range potential due to the permanent dipole moment of formamide. We obtained the well-characterized π* shape resonance located at around 2.38 eV, which belongs to the A″ symmetry of the Cs point group. Our integral and differential cross sections for collisions of electrons were compared with the data available in the literature and showed a good qualitative agreement. To the best of our knowledge, no experimental and theoretical data are currently available for positron-formamide collision, so our present cross sections were compared with the cross sections of formic acid, which is also polar and is isoeletronic to formamide.

Determining cross sections from transport coefficients using deep neural networks

We present a neural network for the solution of the inverse swarm problem of deriving cross sections from swarm transport data. To account for the uncertainty inherent to this somewhat ill-posed inverse problem, we train the neural network using cross sections from the LXCat project, paired with associated transport coefficients found by the numerical solution of Boltzmann’s equation. The use of experimentally measured and theoretically calculated cross sections for training encourages the network to avoid unphysical solutions, such as those containing spurious energy-dependent oscillations. We successfully apply this machine learning approach to simulated swarm data for electron transport in helium, separately determining its elastic momentum transfer and ionisation cross sections to within an accuracy of 4% over the range of energies considered. Our attempt to extend our method to argon was less successful, although the reason for that observation is well-understood. Finally, we explore the feasibility of simultaneously determining cross sections of helium using this approach. We have some success here, determining elastic, total n = 2 excitation and ionisation cross sections to 10%, 20% and 25% accuracy, respectively. We are unsuccessful in properly unfolding the separate n = 2 singlet and triplet excitation cross sections of helium, but this is as expected given their similar threshold energies.

Elastic and inelastic low-energy electron collisions with PH2, PF2 and PCl2 radicals

Ab initio scattering calculations for low-energy electron collisions with PH2, PF2, and PCl2 are performed using the R-matrix method in this study. The elastic integral, differential, and momentum transfer cross sections and the excitation cross sections from the ground state to the five low-lying electron excited states are presented in the energy region of 0.01–15 eV. The target states are represented by including correlations via a configuration interaction technique. The resonant states are detected and identified. The sensitivity of the results to changes in the theoretical model is checked by comparing predictions from a variety of approximations including static exchange, one state close-coupling (CC), and many-state CC approximations. The similarities and differences among the resonances of these three radicals are discussed.

Electron impact cross sections for carbon monoxide and their importance in the electron kinetics of CO2–CO mixtures

This work proposes a complete and consistent set of cross sections for electron impact collisions with carbon monoxide (CO), to be published in the IST-Lisbon database with LXCat. The set is validated by comparing swarm parameters calculated using the two-term Boltzmann solver LoKI-B with available experimental data. A severe inconsistency between the total rotational and effective cross sections reported in the literature for low values of the electron energy (ϵ < 0.1 eV) is pointed out. It is shown that inelastic and superelastic collisions involving rotationally excited levels, as well as superelastic collisions with the first vibrational excited level, have to be taken into account to accurately calculate the electron energy distribution function. The relevance of these mechanisms implies a dependence of the effective momentum transfer cross section on the gas and vibrational temperatures and suggests its replacement by an elastic momentum transfer cross section. The electron kinetics in CO2–CO mixtures are also discussed in detail, namely the influence of vibrational excitation and of the CO2/CO ratio on the electron energy distribution function, rate coefficients and power transfer. The vibrational temperatures of both CO and the different vibrational modes of CO2 have a marked influence on the results, due to the importance of superelastic collisions with the vibrationally excited states of both gases. The presence of CO in the mixture modifies the energy transfer pathways and, at moderate reduced electric fields (∼30−100 Td), the vibrational excitation of CO can become the dominant energy loss mechanism, affecting the input of electron energy into the asymmetric stretching mode of CO2.

Identification of characteristic features in scattering cross sections for the electrons colliding with silver, platinum, and gold atoms

A semi-relativistic approach is employed to calculate elastic differential, integral, and momentum transfer cross sections as well as total (elastic plus inelastic) cross sections for the scattering of electrons from silver, platinum, and gold atoms in the energy range 0.1–100 eV. The projectile-target interaction is composed of real (i.e. the sum of static, exchange, and polarization) and imaginary (i.e. absorption) potential. The total optical potential is then used in the solution of the Dirac equation for the scattered electrons. The characteristic features [Ramsauer-Townsend (RT) minimum and shape resonance] which are required for the fundamental understanding of the dynamic processes at the atomic level, are identified in the low energy region. The value of the RT minimum has been correlated with the scattering length to the dipole polarizability of the target atom. The calculated cross sections are compared with available theoretical calculations and experimental measurements in this energy region.

Positron Scattering from Gas-Phase Beryllium and Magnesium: Theory, Recommended Cross Sections, and Transport Simulations

Results from the application of our optical potential and relativistic optical potential models to positron scattering from gas-phase beryllium (Be) and magnesium (Mg) are presented. Specifically, total cross sections and integral cross sections for the elastic, positronium formation, summed discrete electronic-state excitation, and ionization scattering processes are reported for both species and over an extended incident positron energy range. Where possible, these results are compared against the existing theoretical and experimental data, although it must be noted here that no current measurements are yet available for Be and those that are available for Mg are largely restricted to the total cross section. Nonetheless, on the basis of that comparison, recommended cross section datasets, for all the aforementioned cross sections, are formed. Those recommended cross section data are subsequently employed in a Boltzmann equation analysis to simulate the transport of positrons, under the influence of an applied (external) electric field, through the background Be and Mg gases. Note that relativistic optical potential results for the elastic momentum transfer cross section are also reported, to allow us to account for anisotropy effects in our transport simulations. Finally, our positron simulation results for quantities such as the ionization rate coefficients and flux and bulk drift velocities are compared with the corresponding electron transport results with significant differences being observed.

Evaluation of angular scattering models for electron-neutral collisions in Monte Carlo simulations

In Monte Carlo simulations of electron transport through a neutral background gas, simplifying assumptions related to the shape of the angular distribution of electron-neutral scattering cross sections are usually made. This is mainly because full sets of differential scattering cross sections are rarely available. In this work simple models for angular scattering are compared to results from the recent quantum calculations of Zatsarinny and Bartschat for differential scattering cross sections (DCS’s) from zero to 200 eV in argon. These simple models represent in various ways an approach to forward scattering with increasing electron energy. The simple models are then used in Monte Carlo simulations of range, straggling, and backscatter of electrons emitted from a surface into a volume filled with a neutral gas. It is shown that the assumptions of isotropic elastic scattering and of forward scattering for the inelastic collision process yield results within a few percent of those calculated using the DCS’s of Zatsarinny and Bartschat. The quantities which were held constant in these comparisons are the elastic momentum transfer and total inelastic cross sections.

Collisions of slow electrons withSiF4andGeF4: Shape resonance, Ramsauer-Townsend minimum, and virtual state

We report calculated elastic integral, differential, and momentum transfer cross sections for electron impact with the tetrahalides ${\mathrm{SiF}}_{4}$ and ${\mathrm{GeF}}_{4}$. The cross sections were computed with the Schwinger multichannel method with pseudopotentials in the static-exchange and static-exchange plus polarization approximations and for energies up to 12 eV. Our results are compared with theoretical and experimental results available in the literature, and in general the agreement is quite good. In addition, we report the presence of a Ramsauer-Townsend minimum and of a ${T}_{2}$ shape resonance in the integral cross section of ${\mathrm{SiF}}_{4}$, and the presence of a virtual state and also of a ${T}_{2}$ shape resonance in the ${\mathrm{GeF}}_{4}$ cross section. These features were also observed and discussed by some experiments and calculations.

Modeling elastic momentum transfer cross-sections from mobility data

In this letter we present a new method to simply obtain the elastic momentum transfer cross-section which predicts a maximum of reduced mobility and its sensitivity to the temperature variation at low energies. We first determined the transport cross-section which resembles mobility data for similar closed-shell systems by using the Monte Carlo method. Second, we selected the most probable reactive processes and compiled cross-sections from experimental and theoretical data. At the end, an elastic momentum transfer cross-section is obtained by subtracting the compiled cross-sections from the momentum transfer cross-section, taking into account the effects of the angular scattering distributions. Finally, the cross-section set determined in such a way is used as an input in a final Monte Carlo code run, to calculate the flux and bulk reduced mobility for Ne+ + CF4 which were discussed as functions of the reduced electric field E/N (N is the gas density) for the temperature T = 300 K.

Electron collisions with H2CNH using the R-matrix method

The R-matrix approach is used to calculate the elastic differential, integral, and momentum transfer cross sections for electron impact on H2CNH within static-exchange-polarization (SEP) and close-coupling (CC) approximations. The electron-impact excitation cross sections from the ground state to the first three low-lying electronic excited states of H2CNH molecule have been also studied for the first time. A shape resonance of 2 A′′ symmetry located at 1.95 eV with a width of 0.56 eV is detected within CC model. The effective collision frequencies over a wide electron temperature range (200−30 000 K) are calculated using the data of the momentum-transfer cross section.

Modified effective range analysis of electron scattering from krypton

The elastic cross sections for electron scattering on krypton from zero energy up to 10 eV have been analyzed by the modified effective range method. A simple model based on the analytical solution of the Schrödinger equation with the polarization potential using explicitly determined scattering phase shifts for the three lowest partial waves describes the elastic differential, integral and momentum transfer cross sections up to the energy threshold of the first inelastic process well. In detail, the contribution of the long-range polarization potential to the scattering phase shift is exactly expressed, while the contribution of the short-range effects is modelled by simple quadratic expressions (the effective range expansions). The effective range parameters are determined empirically by comparison with the latest experimental differential cross sections. Presently, the calculated integral and momentum transfer cross sections are validated against numerous electron scattering experiments and the most recent quantum-mechanical theories. To complete the picture, the two-term Boltzmann analysis is employed to determine the electron transport coefficients; the agreement with the electron swarm experimental data is found to be very good.